Conditional generative modeling remains a challenging problem in semi-supervised settings where labeled data is scarce but unlabeled samples are abundant. To effectively leverage structural information embedded within the unlabeled dataset and compensate for sparse conditioning signals, we propose a semi-supervised framework combining conditional stochastic interpolation with low-dimensional latent representations. RepG decomposes generation into two stages: label-dependent latent sampling and high-dimensional reconstruction. This isolates the supervised learning of conditional dependencies to a low-dimensional space, requiring few labels while utilizing the abundant unlabeled data purely for reconstruction. Theoretically, we establish an error decomposition showing that the Kullback-Leibler divergence of RepG comprises stage-wise estimation errors and a structural bias quantified by conditional mutual information. For deep neural network estimators, we derive non-asymptotic convergence rates proving that RepG significantly improves sample complexity. By confining the supervised estimation burden to the low intrinsic dimension of the latent representation, RepG achieves a strictly faster convergence rate. Complemented by a minimax lower bound, our theoretical results demonstrate that this method effectively mitigates the curse of dimensionality inherent in direct ambient-space generative modeling.
Smart manufacturing processes are often installed with a large number of sensors, imaging devices and computers, which not only enable instant communication across various modules of a production system but also aid in intelligent manufacturing management. In this paper, we introduce MODERN, a deep learning framework for quality monitoring and fault isolation, which integrates these enhanced capabilities into the practice of industrial quality control. Using the architecture of an inception residual neural network, we develop a control chart that monitors the likelihood of a product containing defects. We also propose a faulty region estimator that identifies the defective area using transfer learning. To extend our framework to cases where there are not sufficient training data, we suggest a transfer monitoring technique that requires only a small sample size and a hypothesis testing approach for quantitatively assessing the applicability of our method. Theoretically, we establish the minimax optimal convergence rate for both our defect likelihood estimation and fault diagnosis. Our results lead to a seemingly counter-intuitive managerial implication - it may not always be in a manufacturer's best interests to keep upgrading its monitoring equipment regardless of the cost. Empirically, we demonstrate the superior performance of our method in comparison with a state-of-the-art approach using both simulated experiments and real data.
Yicheng Kang, Yuling Jiao, Xin Geng et al.· 0 citations